Some 1,400 Palestinians and 13 Israelis were killed in the fighting that erupted when Israel launched a massive military offensive on Gaza on December 27, in response to rocket firing by Palestinian militants.
A recent 575-page report by a UN team led by South African judge Richard Goldstone accused both Israel and Palestinian armed groups of committing war crimes and possible crimes against humanity during the conflict.
Ban "calls upon all of the parties to carry out credible domestic investigations into the conduct of the conflict without delay," UN Under Secretary General Lynn Pascoe told the Security Council.
Britain, France and the United States backed the appeal.
"We urge the Israeli government to carry out full, credible and impartial investigations into the allegations reported in the Goldstone Report," Britain's outgoing UN Ambassador John Sawers told the council.
"We believe that the parties must now launch independent inquiries in line with international standards on the alleged violations of international humanitarian law and human rights during the Gaza crisis," his French counterpart Gerard Araud said.
US deputy ambassador Alejandro Wolff, whose country is Israel's staunchest ally, reiterated Washington's "serious concerns about the report, its unbalanced focus on Israel, the overly broad scope of its recommendations, and its sweeping conclusions of law."
But Wolff also made clear that Washington took "the allegations in the report seriously.
"Israel has the institutions and the ability to carry out serious investigations of these allegations and we encourage it to do so," he noted.
The remarks came as the Security Council discussed the Goldstone report at its regular monthly meeting on the Middle East, a day before the UN Human Rights Council reopens its own debate on the issue in Geneva.
No resolution was expected to result from the Security Council debate.
Representatives of more than 40 countries took the floor, including several from Arab, nonaligned and Islamic nations who denounced Israel's alleged war crimes in Gaza, its "collective punishment" of the civilian population there and its recent "provocations in occupied East Jerusalem."
But Israel's UN Ambassador Gabriela Shalev renewed her country's total rejection of the report, after the Jewish state again warned that the report's endorsement would sink any chance of restarting Middle East peace talks.
"I regret to say that the Goldstone report is one-sided, biased and therefore wrong -- just as the forum and mandate that established its mission," she said.
The report recommended its conclusions be forwarded to the International Criminal Court prosecutor in The Hague if Israel and Hamas fail to carry out credible investigations within six months.
Neither Israel nor Hamas, which rules Gaza, cooperated with the Goldstone team.
"For those of us who seek to resume the peace process in the Middle East, debating the Goldstone report in the Security Council is but a tale full of sound and fury, signifying nothing," Shalev said.
"If Israel is asked to take further risks for peace, the international community must recognize our right to self-defense," she warned.
The Goldstone report specifically accuses Israel of disproportionate use of force and of failing to protect civilians during its military onslaught on the Palestinian enclave.
In his address to the council, Palestinian foreign minister Riyad al-Malki urged the Security Council, the General Assembly and the International Criminal Court to implement the Goldstone report's recommendations.
He also expressed hope that the Geneva-based Human Rights Council (HRC), which is to debate the report Thursday and possibly Friday, would endorse its recommendations.
"We hope that the countries tomorrow and the day after in the HRC will adhere to the report and will endorse its recommendations, so the report might come again to the Security Council and this time we'll have a serious discussion," he told reporters.
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